Introduction to Mathematical Physics/Relativity/Introduction

In this chapter we focus on the ideas of symmetry and transformations. More precisely, we study the consequences on the physical laws of transformation invariance. The reading of the appendices Tensors and  Groups is thus recommended for those who are not familiar with tensorial calculus and group theory. In classical mechanics, a material point of mass $$m$$ is referenced by its position $$r$$ and its momentum $$p$$ at each time $$t$$. Time does not depend on the reference frame used to evaluate position and momentum. The Newton's law of motion is invariant under Galileean transformations. In special and general relativity, time depends on the considered reference frame. This yields to modify classical notions of position and momentum. Historicaly, special relativity was proposed to describe the invariance of the light speed. The group of transformations that leaves the new form of the dynamics equations is the Lorentz group. Quantum, kinetic, and continuous description of matter will be presented later in the book. .